Grassmann bundle
In algebraic geometry, the Grassmann d-plane bundle of a vector bundle E on an algebraic scheme X is a scheme over X: p : G d ( E ) → X {\displaystyle p:G_{d}(E)\to X} such that the fiber p − 1 ( x ) = G d ( E x ) {\displaystyle p^{-1}(x)=G_{d}(E_{x})} is the Grassmannian of the d-dimensional vector subspaces of E x {\displaystyle E_{x}} . For example, G 1 ( E ) = P ( E ) {\displaystyle G_{1}(E)=\mathbb {P} (E)} is the projective bundle of E. In the other direction, a Grassmann bundle is a special case of a (partial) flag bundle.